Physicists May Have Answered a Twenty-Year-Old Riddle Called 3.7 Sigma

Modern science has centered around one mathematical equation for decades: the “Standard Model.” Using twelve types of matter particles, three forces, and a special binding agent called the Higgs-Boson, the Standard Model does its best—and its best is pretty good—to explain the physical universe. It assumes the ideas of Quantum Field Theory, which suggest reality is not made of tiny particles but of fields, which dance through the universe in a harmonious ode to the laws of physics. These fields interplay to create the visible world as two kinds of particles: fermions and bosons. 

Fermions make up matter; bosons carry forces which act on matter, such as gravity. A rule called Pauli’s exclusion principle divides the two, using the intricate world of quantum mechanics to try to explain what any child can see—that no two objects can be in the same space at the same time. In other words, Pauli’s principle says stubbing your toe hurts because the fermions in your leg bump against the fermions in the leg of your grandmother’s armchair. In such a scenario, bosons are also present as the electric energy particles that carry a nerve signal of pain to your brain. 

However, one fermion has acted so strangely that the Standard Model may soon have to give way to new physics. 

The current particle family is defined by its three eldest children: the electron and the up and down quarks. These last two, like ingredients in a cooking recipe, form the better-known proton and neutron. Two up quarks and a down make a proton; two down quarks and an up make a neutron—no baking required. Further recipes tell us that combining these protons and neutrons make nuclei, that adding electrons to those nuclei results in atoms, and that adding more atoms to those ones results in skin, bones, and organs—our bodies. 

But these three particles have a fourth, recalcitrant sibling: the neutrino. Neutrinos are the ghosts of the particle world, being so light they hardly ever interact with other fermions. Hailing from the beginnings of the universe, they float on unimpeded cosmic journeys, radiating from the sun and even passing through you as you read this. 

So these four particles—the electron, the up and down quarks, and the neutrino—make up the physical world. However, each of these four has a second and third iteration, resulting in a total of twelve fermions. That is, the electron also appears as the second generation “muon” and third generation “tau” particles. The up and down quarks are similarly echoed as “strange,” “charm,” “bottom,” and “top” quarks. And the ghostlike neutrino has twin siblings, the “muon” and “tau” neutrinos. This beautiful harmony can be seen, along with four blue bosons and the unifying, purple Higgs-Boson, in a circular diagram of the Standard Model. 

A wheel describing the Standard Model. Courtesy of Symmetry Magazine

The Model is simple yet mysterious because these three generations of fermions vary only by weight. For example, a muon has the same electric charge and spin rate as an electron, but is 200x heavier. As such, the muon can carry more energy, giving it the potential to open windows into the subatomic world, which at times is as murky as the bottom of the sea. Ultimately, the Model is an enticing half-mystery because our understanding of its particle families is so peculiar. For instance, we know a particle such as the neutrino cannot exist without its three counterparts, the electron and the up and down quarks. But we have no idea why there are precisely three generations of these four particles—it’s a mystery locked in the beauty of creation. 

And so, it seems, might be the possibility of other, undiscovered particles. In 2001, muons racing inside a magnetic storage ring at Brookhaven National Laboratory behaved so strangely that for the next two decades, physicists around the world would ponder the riddle of “3.7 Sigma.” 

The name, arising from statistics, indicates odds of about one-in-4500 that the muons’ behavior was due to random chance—a 99.98% probability of a new scientific discovery. Excitement stirred; everyone wondered if strange particles were affecting the microworld. Old physics was prepared to be tossed out the window. For the past three years, Fermi National Laboratory in Illinois has performed the Muon g-2 experiment in an attempt to solve the mystery—and the results are deeply surprising.

“If you imagine flipping a coin a hundred times,” explained Chris Polly, particle physicist with the experiment, “[3.7 Sigma] would be about like finding 67 heads or 68 heads, something like that. And you think, ‘Well, that’s kind of weird. I wonder if there’s something wrong with the coin.’ The goal was to… do the experiment again at a laboratory capable of producing twenty times the number of muons.” 

These muons, spinning in their confinement chamber, each generated their own magnetic field. When these smaller fields interacted with the storage ring’s larger one, the result was a slight wobble to each muon’s spin, known as its “magnetic moment.” Precisely examining this wobble and comparing it to the Standard Model would indicate whether Brookhaven’s result was fancy or fact. As it turns out, the Fermilab g-2 experiment perfectly reproduced the Brookhaven anomaly with an even greater 4.2 sigma discrepancy, an incredible result with a likelihood of one-in-40,000. It looks like new physics might be right on the horizon.

But the situation stands on a knife’s edge. A scientific paper published at the same time suggests this wobble is exactly what the Standard Model describes. If the authors, known as BMW (Budapest-Marseille-Wuppertal, not the auto company), have their supercomputer calculations right, a mysterious number in Standard Model muon calculations is slightly larger than the value accepted by the Muon g-2 overseers. This theoretical value seems to predict the wobble far better. Chaos ensued. 

This idea of a new value was not new—it first appeared in an unevaluated paper in February, 2020. Aida El-Khadra, theoretical particle physicist at the University of Illinois, said the “Theory Initiative” helping to interpret the Muon g-2 experiment was aware of this calculation but did not consider it because no third party had verified the result. “We need to have a close look at the calculation,” she said. “It is pushing on the methods to get that precision, and we need to understand if the way they pushed on the methods broke them.”

But if BMW is right about muon calculations, the possibility of new physics could be closed behind a wall of mystery and unclear data trends, disappointing scores of scientists and twenty years of breathless research. If BMW is wrong, however, Muon g-2 might just herald one of the greatest discoveries in particle physics to date. 

“This is a very sensitive and interesting situation,” said Zoltan Fodor, one of the BMW theorists. “We cross-checked [our result] a million times because we were very much surprised.”

There’s no telling where particle physics will go in the future, for the sinewy strength of reality deadens data, frustrates research, and spawns errors like countless sparks leaping into the night sky of the observable universe. But enticing possibilities glimmer on the edge of our view, evading capture. Perhaps humanity will be permitted to access them, as we were permitted to walk on the moon. No matter what the future holds, the ordered beauty of the fermions—flourishing in the Standard Model like twelve petals of a sundazzled flower—will remain, hands linked in a circle dance to the symphony of the laws of physics.



Hartnett, K. (2021, July 16). A video tour of the standard model | quanta magazine. Quanta Magazine.

Hossenfelder, S. (2021, April 7). Is the standard model of physics now broken? Scientific American.

Moyer, M. (2021, December 22). The Year in physics. Quanta Magazine.

Wiltfong, R. (Ed.). (n.d.). Muon g-2 Theory Initiative. Home | Muon g-2 Theory. Retrieved January 23, 2022, from

Riesselmann, K. (2015, July 21). The standard model of particle physics. Symmetry Magazine.

Wolchover, N. (2021, April 7). ‘Last Hope’ Experiment Finds Evidence for Unknown Particles. Quanta Magazine.

Images courtesy of Symmetry Magazine and Science & Society Picture Library/SSPL via Getty 



  1. I LOVE quantum mechanics so this was a delight to read, besides just being fascinating! Enough to make your head spin, but on the other hand… so cool XD

    • Thank you! And yes, my head spun like a top. Chris Polly does such a great job explaining these complicated concepts to people like you and me.

  2. 😀 Awesome!! I’ve always wanted to learn more about quantum physics, especially because the field is still having discoveries! Good job!

    • Thank you, and you’re very right! A lot of researchers are saying that even if this anomaly turns out to be predicted by the Standard Model, there are still many other discrepancies that point to the existence of new particle physics. So I hope you find that as exciting as I do, and thanks for commenting!

  3. 🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯